Precalculus

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The Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Counting and Probability; A Preview of Calculus; and more. For individuals with an interest in learning Precalculus as it applies to their everyday lives.

Preface to the Instructor

ix

(4)

Preface to the Student

xiii

(10)

List of Applications

xxiii

(4)

Photo Credits

xxvii

CHAPTER 1 EQUATIONS AND GRAPHS

1

(100)

1.1 Topics from Algebra and Geometry

3

(14)

1.2 Solving Equations

17

(8)

1.3 Setting Up Equations: Applications

25

(13)

1.4 Inequalities

38

(15)

1.5 Rectangular Coordinates; Graphs; Circles

53

(19)

1.6 Lines

72

(14)

1.7 Linear Curve Fitting

86

(7)

Chapter Review

93

(8)

CHAPTER 2 FUNCTIONS AND THEIR GRAPHS

101

(78)

2.1 Functions

103

(19)

2.2 More about Functions

122

(17)

2.3 Graphing Techniques: Transformations

139

(13)

2.4 Operations on Functions; Composite Functions

152

(10)

2.5 Mathematical Models: Constructing Functions

162

(10)

Chapter Review

172

(7)

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS

179

(106)

3.1 Quadratic Functions; Curve Fitting

181

(19)

3.2 Polynomial Functions

200

(17)

3.3 Rational Functions

217

(25)

3.4 Synthetic Division

242

(4)

3.5 The Real Zeros of a Polynomial Function

246

(17)

3.6 Complex Numbers; Quadratic Equations with a Negative Discriminant

263

(9)

3.7 Complex Zeros; Fundamental Theorem of Algebra

272

(7)

Chapter Review

279

(6)

CHAPTER 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

285

(82)

4.1 One-to-One Functions; Inverse Functions

287

(11)

4.2 Exponential Functions

298

(13)

4.3 Logarithmic Functions

311

(9)

4.4 Properties of Logarithms; Curve Fitting

320

(13)

4.5 Logarithmic and Exponential Equations

333

(7)

4.6 Compound Interest

340

(9)

4.7 Growth and Decay

349

(8)

4.8 Logarithmic Scales

357

(5)

Chapter Review

362

(5)

CHAPTER 5 TRIGONOMETRIC FUNCTIONS

367

(88)

5.1 Angles and Their Measure

369

(11)

5.2 Trigonometric Functions: Unit Circle Approach

380

(15)

5.3 Properties of the Trigonometric Functions

395

(12)

5.4 Right Triangle Trigonometry

407

(12)

5.5 Graphs of the Trigonometric Functions

419

(11)

5.6 Sinusoidal Graphs; Sinusoidal Curve Fitting

430

(18)

Chapter Review

448

(7)

CHAPTER 6 ANALYTIC TRIGONOMETRY

455

(64)

6.1 Trigonometric Identities

457

(6)

6.2 Sum and Difference Formulas

463

(9)

6.3 Double-angle and Half-angle Formulas

472

(10)

6.4 Product-to-Sum and Sum-to-Product Formulas

482

(4)

6.5 The Inverse Trigonometric Functions

486

(16)

6.6 Trigonometric Equations

502

(12)

Chapter Review

514

(5)

CHAPTER 7 APPLICATIONS OF TRIGONOMETRIC FUNCTIONS

519

(48)

7.1 Solving Right Triangles

521

(10)

7.2 The Law of Sines

531

(11)

7.3 The Law of Cosines

542

(7)

7.4 The Area of a Triangle

549

(7)

7.5 Simple Harmonic Motion; Damped Motion

556

(6)

Chapter Review

562

(5)

CHAPTER 8 POLAR COORDINATES; VECTORS

567

(72)

8.1 Polar Coordinates

569

(8)

8.2 Polar Equations and Graphs

577

(17)

8.3 The Complex Plane; De Moivre's Theorem

594

(10)

8.4 Vectors

604

(11)

8.5 The Dot Product

615

(10)

8.6 Vectors in Space

625

(10)

Chapter Review

635

(4)

CHAPTER 9 ANALYTIC GEOMETRY

639

(68)

9.1 Conics

641

(1)

9.2 The Parabola

642

(10)

9.3 The Ellipse

652

(12)

9.4 The Hyperbola

664

(12)

9.5 Rotation of Axes; General Form of a Conic

676

(8)

9.6 Polar Equations of Conics

684

(5)

9.7 Plane Curves and Parametric Equations

689

(13)

Chapter Review

702

(5)

CHAPTER 10 SYSTEMS OF EQUATIONS AND INEQUALITIES

707

(100)

10.1 Systems of Linear Equations: Substitution; Elimination

709

(13)

10.2 Systems of Linear Equations: Matrices

722

(16)

10.3 Systems of Linear Equations: Determinants

738

(12)

10.4 Matrix Algebra

750

(18)

10.5 Partial Fraction Decomposition

768

(7)

10.6 Systems of Nonlinear Equations

775

(10)

10.7 Systems of Inequalities

785

(8)

10.8 Linear Programming

793

(8)

Chapter Review

801

(6)

CHAPTER 11 SEQUENCES; INDUCTION; COUNTING; PROBABILITY

807

(76)

11.1 Sequences

809

(9)

11.2 Arithmetic Sequences

818

(6)

11.3 Geometric Sequences; Geometric Series

824

(12)

11.4 Mathematical Induction

836

(4)

11.5 The Binomial Theorem

840

(9)

11.6 Sets and Counting

849

(5)

11.7 Permutations and Combinations

854

(11)

11.8 Probability

865

(10)

Chapter Review

875

(8)

CHAPTER 12 A PREVIEW OF CALCULUS: THE LIMIT AND THE DERIVATIVE OF A FUNCTION